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As one of the fundamental vehicular perception technologies, millimeter-wave radar's accuracy in angle measurement affects the decision-making and control of vehicles. In order to enhance the accuracy and efficiency of the Direction of Arrival (DoA) estimation of radar systems, a super-resolution angle measurement strategy based on the Fast Deterministic Maximum Likelihood (FDML) algorithm is proposed in this paper. This strategy sequentially uses Digital Beamforming (DBF) and Deterministic Maximum Likelihood (DML) in the Field of View (FoV) to perform a rough search and precise search, respectively. In a simulation with a signal-to-noise ratio of 20 dB, FDML can accurately determine the target angle in just 16.8 ms, with a positioning error of less than 0.7010. DBF, the Iterative Adaptive Approach (IAA), DML, Fast Iterative Adaptive Approach (FIAA), and FDML are subjected to simulation with two targets, and their performance is compared in this paper. The results demonstrate that under the same angular resolution, FDML reduces computation time by 99.30 % and angle measurement error by 87.17 % compared with the angular measurement results of two targets. The FDML algorithm significantly improves computational efficiency while ensuring measurement performance. It provides more reliable technical support for autonomous vehicles and lays a solid foundation for the advancement of autonomous driving technology. [ABSTRACT FROM AUTHOR]

For high‐resolution radar, traditional direction of arrival (DOA) angle measuring algorithms for point‐like targets cannot be directly applied to extended targets. Instead, pixel‐based detection and clustering must be performed first, followed by angle estimation. However, the presence of factors such as clutter and system noise makes it impossible to guarantee a one‐to‐one correspondence between the multiple scattering points of an extended target and the real target, which may result in significant discrepancies between the angle estimation and localization results and the real target. To address this issue, this paper proposes and discusses a radar extended target arrival angle estimation method based on effective phase clustering. The proposed method selects effective target scatterers through the interferometric phase information between channels, clusters these points, and then estimates the DOA angle of the extended target, effectively reducing the impact of interference scatterers on DOA angle estimation and improving the angular measurement accuracy. The effectiveness of the proposed method was validated by the measured data obtained from an airborne digital beamforming radar system. [ABSTRACT FROM AUTHOR]

The tensor‐based spatial smoothing is a good algorithm for the direction of arrival (DOA) estimation, but it cannot make good use of the physical aperture of the array, so the paper proposes a tensor‐based array virtual translation DOA estimation algorithm to solve the problem. Under the framework of tensor‐based DOA estimation algorithm, the factor matrix obtained by tensor decomposition is extended to a signal subspace with Vandermonde structure by using array virtual translation technology. In addition, the algorithm expands the available array aperture, breaks through the limitation of physical array aperture on multi‐target estimation ability, and further improves the estimation accuracy. Since the processing technique proposed in this paper has nothing to do with the construction of tensors, this technique is suitable for conventional DOA estimation algorithms based on tensors. Theoretical analysis and simulation experiments verify the effectiveness of the algorithm proposed in this paper. [ABSTRACT FROM AUTHOR]

In this paper, we explore the problem of direction-of-arrival (DOA) estimation for a non-uniform linear array (NULA) under strong noise. The compressed sensing (CS)-based methods are widely used in NULA DOA estimations. However, these methods commonly rely on the tuning of parameters, which are hard to fine-tune. Additionally, these methods lack robustness under strong noise. To address these issues, this paper proposes a novel DOA estimation approach using a deep neural network (DNN) for a NULA in a low SNR. The proposed network is designed based on the denoising convolutional neural network (DnCNN) and the alternating direction method of multipliers (ADMM), which is dubbed as LDnADMM-Net. First, we construct an unfolded DNN architecture that mimics the behavior of the iterative processing of an ADMM. In this way, the parameters of an ADMM can be transformed into the network weights, and thus we can adaptively optimize these parameters through network training. Then, we employ the DnCNN to develop a denoising module (DnM) and integrate it into the unfolded DNN. Using this DnM, we can enhance the anti-noise ability of the proposed network and obtain a robust DOA estimation in a low SNR. The simulation and experimental results show that the proposed LDnADMM-Net can obtain high-accuracy and super-resolution DOA estimations for a NULA with strong robustness in a low signal-to-noise ratio (SNR). [ABSTRACT FROM AUTHOR]

This paper presents a wideband signal (WS) beamforming method based on Inception convolutional neural network (ICNN), named as WS-ICNN algorithm. Firstly, an Inception module is constructed via some convolutional layers with feature maps of different sizes and a pooling layer. It can not only extract different scale information of covariance matrix, but also excavate the spatial correlation information about received wideband signals, so that the inception module can help neural network improve the beamforming output performance. On this basis, an ICNN model is established, which is suitable for wideband beamforming. Then, in order to obtain a good training label for the proposed ICNN model, a taper matrix and a second-order cone programming problem are introduced to calculate a wideband beamforming weight vector label. Based on this label, the training process of the proposed ICNN model is accomplished. Finally, the well-trained ICNN model accepts the input of the covariance matrix, and output the beamforming weight vector. Simulation results demonstrate the performance of the proposed algorithm in the cases of direction-of-arrival estimation error and sensor position error. [ABSTRACT FROM AUTHOR]

Today, the common solutions for underwater source angle detection require manned vessels and towed arrays, which are associated with high costs, risks, and deployment difficulties. An alternative solution for such applications is represented by acoustic vector sensors (AVSs), which are compact, lightweight and moderate in cost, and which have promising performance in terms of the bearing discrimination in two or three dimensions. One of the most popular devices for passive monitoring in underwater surveillance systems that employ AVSs is the directional frequency analysis and recording (DIFAR) sonobuoy. In this paper, direct data-processing (DDP) algorithms are implemented to calculate the azimuth angle of underwater acoustic sources by using short-time Fourier transform (STFT) via the arctan method instead of using fast Fourier transform (FFT). These algorithms for bearing estimation use the 'Azigram' to plot the estimated bearing of a source. It is demonstrated that by knowing the active sound intensity of the sound field and applying the inverse tangent to its real part, this matrix can be obtained. Announcing the time and frequency of the source simultaneously is one of the main advantages of this method, enabling the detection of multiple sources concurrently. DDP can also provide more details about sources' characteristics, such as the frequency of the source and the time of the source's presence. [ABSTRACT FROM AUTHOR]

As one of the most widely used spread spectrum techniques, the frequency-hopping spread spectrum (FHSS) has been widely adopted in both civilian and military secure communications. In this technique, the carrier frequency of the signal hops pseudo-randomly over a large range, compared to the baseband. To capture an FHSS signal, conventional non-cooperative receivers without knowledge of the carrier have to operate at a high sampling rate covering the entire FHSS hopping range, according to the Nyquist sampling theorem. In this paper, we propose an adaptive compressed method for joint carrier and direction of arrival (DOA) estimations of FHSS signals, enabling subsequent non-cooperative processing. The compressed measurement kernels (i.e., non-zero entries in the sensing matrix) have been adaptively designed based on the posterior knowledge of the signal and task-specific information optimization. Moreover, a deep neural network has been designed to ensure the efficiency of the measurement kernel design process. Finally, the signal carrier and DOA are estimated based on the measurement data. Through simulations, the performance of the adaptively designed measurement kernels is proved to be improved over the random measurement kernels. In addition, the proposed method is shown to outperform the compressed methods in the literature. [ABSTRACT FROM AUTHOR]

Acoustic vector sensor (AVS) is a kind of sensor widely used in underwater detection. Traditional methods use the covariance matrix of the received signal to estimate the direction-of-arrival (DOA), which not only loses the timing structure of the signal but also has the problem of weak anti-noise ability. Therefore, this paper proposes two DOA estimation methods for underwater AVS arrays, one based on a long short-term memory network and attention mechanism (LSTM-ATT), and the other based on Transformer. These two methods can capture the contextual information of sequence signals and extract features with important semantic information. The simulation results show that the two proposed methods perform much better than the multiple signal classification (MUSIC) method, especially in the case of low signal-to-noise ratio (SNR), the DOA estimation accuracy has been greatly improved. The accuracy of the DOA estimation method based on Transformer is comparable to that of the DOA estimation method based on LSTM-ATT, but the computational efficiency is obviously better than that of the DOA estimation method based on LSTM-ATT. Therefore, the DOA estimation method based on Transformer proposed in this paper can provide a reference for fast and effective DOA estimation under low SNR. [ABSTRACT FROM AUTHOR]

In this paper, two approaches are proposed for estimating the direction of arrival (DOA) and power spectral density (PSD) of stationary point sources by using a single, rotating, directional microphone. These approaches are based on a method previously presented by the authors, in which point source DOAs were estimated by using a broadband signal model and solving a group-sparse optimization problem, where the number of observations made by the rotating directional microphone can be lower than the number of candidate DOAs in an angular grid. The DOA estimation is followed by the estimation of the sources' PSDs through the solution of an overdetermined least squares problem. The first approach proposed in this paper includes the use of an additional nonnegativity constraint on the residual noise term when solving the group-sparse optimization problem and is referred to as the Group Lasso Least Squares (GL-LS) approach. The second proposed approach, in addition to the new nonnegativity constraint, employs a narrowband signal model when building the linear system of equations used for formulating the group-sparse optimization problem, where the DOAs and PSDs can be jointly estimated by iterative, group-wise reweighting. This is referred to as the Group-Lasso with l 1 -reweighting (GL-L1) approach. Both proposed approaches are implemented using the alternating direction method of multipliers (ADMM), and their performance is evaluated through simulations in which different setup conditions are considered, ranging from different types of model mismatch to variations in the acoustic scene and microphone directivity pattern. The results obtained show that in a scenario involving a microphone response mismatch between observed data and the signal model used, having the additional nonnegativity constraint on the residual noise can improve the DOA estimation for the case of GL-LS and the PSD estimation for the case of GL-L1. Moreover, the GL-L1 approach can present an advantage over GL-LS in terms of DOA estimation performance in scenarios with low SNR or where multiple sources are closely located to each other. Finally, it is shown that having the least squares PSD re-estimation step is beneficial in most scenarios, such that GL-LS outperformed GL-L1 in terms of PSD estimation errors. [ABSTRACT FROM AUTHOR]

The underwater maneuvering platform generates self-noise when sailing, which shows spatial directionality to the arrays fixed on the platform. In this paper, it is called spatially colored noise (SCN). The direction of arrival (DOA) estimation results are often influenced by this self-noise, leading to a decrease in estimation accuracy and to the appearance of spurious peaks. To resolve this problem, a sparse Bayesian learning (SBL) method adapted to underwater maneuvering platform noise is proposed in this paper. The SBL framework with unknown SCN is established first. Then, the SCN covariance matrix is estimated by projecting the received data covariance matrix into the noise subspace, and the DOA estimation results are finally obtained through multiple iterations. The simulation results show that the proposed method avoids spurious peaks, and compared to the existing methods, the proposed method achieves a higher accuracy in the case of low SNRs and small snapshot numbers. The sea trial data processing results show that the proposed method provides lower and flatter noise spectrum levels without spurious peaks. [ABSTRACT FROM AUTHOR]

This paper proposes an innovative global solution which is a pioneering work applying automated machine learning algorithms to remarkable precision sparse underwater direction-of-arrival (DOA) estimation that views the subaquatic sparse-sampling DOA estimation problem as a classification prediction task. The proposed solution, termed automated multi-layer perceptron discriminative neural network (AutoMPDNN), is built upon a Bayesian optimization framework. AutoMPDNN transforms sparsely sampled time-domain signals into the complex domain, preserving essential components in a one-source single-snapshot scenario. Leveraging Bayesian optimization principles, the algorithm embeds necessary hyperparameters into the loss function, effectively defining it as a maximum likelihood problem using the upper confidence bound function and incorporating sparse signal features. We also explore the model space architecture and introduce variants of AutoMPDNN, denoted as AutoMPDNNs_ln (n = 2,3,4). Through a series of plane wave simulation experiments, it is demonstrated that AutoMPDNN achieves the highest prediction performance for one-source single-snapshot scenarios compared to classical DOA estimation algorithms that incorporate sparse representation approaches, as well as contemporary deep learning DOA methods under varying conditions. [ABSTRACT FROM AUTHOR]

How to enhance the desired signal with low signal-to-noise ratio (SNR) is a difficult problem in the estimation process of the direction-of-arrival (DOA) of the target scattering wave signal. In this paper, the feasibility of spatial spectrum estimation in the Range-Doppler (RD) domain is analyzed in principle, and the SNR gain expression of weak scattering wave signal is derived when constructing multi-snapshots virtual array data. On this basis, the mutual eigenvector singular value decomposition (MESVD) method based on RD domain mode excitation is proposed, which can robustly and effectively estimate the direction of the coherent weak signals. Simulation experiments verify that the RD domain spectral estimation method has the ability to simultaneously obtain the direction of multiple weak target scattering waves, and the direction-finding accuracy can reach the Cramer–Rao bound (CRB) of conventional spectral estimation method. The results of Monte Carlo experiments show that the root-mean-square-error (RMSE) of azimuth estimation of RD domain spatial spectrum estimation method is 5.76° lower than that of a conventional multiple signal classification (MUSIC) method. In addition, the practicability of the proposed method is demonstrated by comparing the DOA estimation results of a set of real data with Automatic Dependent Surveillance-Broadcast (ADS-B) data. [ABSTRACT FROM AUTHOR]

The estimation of direction of arrival (DOA) is paramount in the realm of practical array signal processing systems. Nevertheless, traditional estimation methods often rely heavily on the Gaussian noise assumption, rendering them ineffective in achieving high-precision estimates in environments plagued by strong impulsive noise. To address this challenge, this paper introduces a novel DOA estimation algorithm that leverages mixed fractional lower-order correntropy (MFLOCR) in the context of Alpha-stable distributed impulsive noise. Correntropy is used as a measure of the similarity of the signals, using a Gaussian function to smooth extreme values and provide greater robustness against impulsive noise. By utilizing diverse kernel lengths to jointly regulate the kernel function, the concept of correntropy is expanded and implemented in the fractional lower-order moment (FLOM) algorithm for received signals. Subsequently, the MFLOCR is derived by adjusting the resulting form of correntropy. Finally, an enhanced DOA estimation algorithm is proposed that combines the MFLOCR operator with the MUSIC algorithm, specifically tailored for impulsive noise environments. Furthermore, a proof of boundedness is provided to validate the effectiveness of the proposed approach in such noisy conditions. Simulation experiments confirmed that the proposed method outperforms existing DOA estimation methods in the context of intense impulsive noise, a low generalized signal-to-noise ratio (GSNR), and a smaller number of snapshots. [ABSTRACT FROM AUTHOR]

Increasing airspace safety is an important challenge, both for unmanned aerial vehicles (UAVs) as well as manned aircraft. Future developments of collision avoidance systems are supposed to utilize information from multiple sensing systems. A compact sensing system could employ a multi-mode multi-port antenna (M   3 PA). Their ability to radiate multiple orthogonal patterns simultaneously makes them suitable for communication applications as well as bearing and ranging applications. Furthermore, they can be designed to flexibly originate near-omnidirectional and/or directional radiation patterns. This option of flexibility with respect to the radiation characteristic is desired for antennas integrated in collision avoidance systems. Based on the aforementioned properties, M   3 PAs represent a compelling option for aircraft transponders. In this paper, direction-of-arrival (DoA) estimation using an M   3 PA designed for aerial applications is put to the test. First, a DoA estimation scheme suitable to be employed with M   3 PAs is introduced. Next, the validity of the proposed method is confirmed through numerical simulations. Lastly, practical experiments are conducted in an antenna measurement chamber to verify the numerical results. [ABSTRACT FROM AUTHOR]

In this paper, an innovative cyclic noise reduction method and an improved CAPON algorithm (also the called minimum variance distortionless response (MVDR) algorithm) are proposed to improve the accuracy and reliability of DOA (direction of arrival) estimation. By processing the eigenvalues obtained from the covariance matrix of the received signal, the signal-to-noise ratio (SNR) can be increased by up to 5 dB by the cyclic noise reduction method, which will improve the DOA estimation accuracy. The improved CAPON algorithm has a convolution neural network (CNN) structure, whose input is the processed covariance matrix of the received signal, and the CAPON spectral value is used as the training label to obtain the estimated spatial spectrum. It retains the advantages of the CAPON algorithm, which can achieve blind source estimation, and simulations show that the proposed algorithm exhibits a better performance than the traditional algorithm in conditions of various SNRs and snapshot numbers. The simulation results show that, based on a certain SNR, the root mean square error (RMSE) of the improved CAPON algorithm can be reduced from 0.86° to 0.8° compared to traditional algorithms, and the angle estimation error can be decreased by up to about 0.3°. With the help of the cyclic noise reduction method, the angle estimation error decreases from 0.04° to 0.02°. [ABSTRACT FROM AUTHOR]

Remote passive sonar detection with underwater acoustic vector sensor (UAVS) has attracted increasing attention due to its merit in measuring the full sound field information. However, the accurate estimation of the direction-of-arrival (DOA) remains a challenging problem, especially under low signal-to-noise ratio (SNR) conditions. In this paper, a novel convolution (COV)-based single-vector acoustic preprocessing method is proposed on the basis of the single-vector acoustic preprocessing model. In view of the theoretical analysis of the classical single-vector acoustic DOA estimation method, the principle of preprocessing can be described as "to achieve an improved denoising performance in the constraint of equivalent amplitude gain and phase response." This can be naturally guaranteed by our proposed COV method. In addition, the upper bound with matched filtering (MF) preprocessing is provided in the consideration of the optimal linear signal processing for weak signal detection under Gaussian noise. Numerical analyses demonstrate the effectiveness of our proposed preprocessing method with both vector array signal processing-based and intensity-based methods. Experimental verification conducted in South China Sea further verifies the effectiveness of our approach for practical applications. This work can lay a solid foundation in improving underwater remote vector acoustic DOA estimation under low SNR, and can provide important guidance for future research work. [ABSTRACT FROM AUTHOR]

The L-band digital aeronautical communication system (LDACS) is one of the candidate technologies for future broadband digital aeronautical communications, utilizing the unused L-band spectrum between distance measuring equipment (DME) channels. However, the higher signal power of DME complicates LDACS implementation. This paper proposes an advanced DME mitigation approach for the LDACS, integrating joint direction of arrival (DOA) estimation with adaptive beamforming techniques. The proposed method begins by exploiting the cyclostationary characteristics of signals, accurately obtaining the preliminary direction of the LDACS signal using the Cyclic-MUSIC method. Subsequent precise steering vectors (SVs) are selected through Capon spectrum search, followed by the reconstruction of the interference plus noise covariance matrix (INCM). Using the obtained SV and INCM, the weight vector is calculated and beamforming is performed. Simulation results validate that the proposed method not only accurately estimates the direction of LDACS signal but also efficiently mitigates DME interference, demonstrating a superior performance and reduced algorithmic complexity, even in scenarios with lower signal-to-noise ratios (SNRs) and the presence of DOA estimation errors. Additionally, the proposed method achieves a low bit error rate (BER), further validating its ability to ensure communication quality and enhance the reliability of LDACS. [ABSTRACT FROM AUTHOR]

Wideband direction-of-arrival (DOA) estimation is an important task for passive sonar signal processing. Nowadays, sparse Bayesian learning (SBL) attracts much attention due to its good performance. However, performance degrades in the existence of strong interference. This problem can be solved by combining the beamformer and the SBL. The beamformer is a useful tool to suppress interference. Then, the SBL can easily estimate the DOA of the targets from the beamformer power outputs (BPO). Unfortunately, the latter step needs to compute the matrix inversion frequently, which brings some computational burden to the sonar system. In this paper, the BPO-based SBL is modified. A sequential solution is provided for the parameters in the BPO probabilistic model. In this manner, only one signal precision parameter involved in the probabilistic model is updated in each iteration and the matrix inversion is avoided during the iteration, thus reducing the computational burden. Simulation and experimental results show that the proposed method maintains high estimation precision in the interference environment. At the same time, its computational efficiency is almost three times higher in comparison with state-of-the-art methods. [ABSTRACT FROM AUTHOR]

In the field of direction of arrival (DOA) estimation for coherent sources, subspace-based model-driven methods exhibit increased computational complexity due to the requirement for eigenvalue decomposition. In this paper, we propose a new neural network, i.e., the signal space deep convolution (SSDC) network, which employs the signal space covariance matrix as the input and performs independent two-dimensional convolution operations on the symmetric real and imaginary parts of the input signal space covariance matrix. The proposed SSDC network is designed to address the challenging task of DOA estimation for coherent sources. Furthermore, we leverage the spatial sparsity of the output from the proposed SSDC network to conduct a spectral peak search for obtaining the associated DOAs. Simulations demonstrate that, compared to existing state-of-the-art deep learning-based DOA estimation methods for coherent sources, the proposed SSDC network achieves excellent results in both matching and mismatching scenarios between the training and test sets. [ABSTRACT FROM AUTHOR]

In this paper, we consider the problem of bearing ambiguity in the direction of arrival (DOA) estimation due to spatial aliasing when the minimum wavelength of the processing broadband signal is less than the element spacing of a uniform linear array (ULA). First, an extended frequency-difference (FD) method is presented. Unlike the existing FD methods, the extended FD signal is constructed by conjugate multiplying a diagonal matrix consisting of steering vectors at high frequency and pre-processing direction with the array sampled signal matrix at low frequency. Then, this paper establishes a decision criterion for distinguishing the aliasing component that varies linearly with frequency in the extended FD space. Finally, an unambiguous broadband DOA estimation method is achieved by suppressing spatial aliasing in the extended FD space. The simulation results show the effectiveness of the proposed method in low signal-to-noise ratio, low signal-to-interference ratio, and multi-interference conditions. The unambiguous processing ability of the proposed method is further verified in the South China Sea using ship signals in the frequency band of 200 to 700 Hz and a 10-element ULA with a 6.25 m spacing deployed on the seabed. [ABSTRACT FROM AUTHOR]

This paper provides a simple yet effective approach to improve direction-of-arrival (DOA) estimation performance in extreme signal-to-noise-ratio (SNR) conditions. As an example, a multiple signal classification (MUSIC) algorithm with a deep learning (DL) approach is used. First, brief research into the existing DOA estimation techniques is provided, followed by a demonstration of a simulation environment created on the MATLAB platform to generate and resolve signals from a uniform rectangular array of antenna elements. Following that is an attempt to improve the estimation accuracy of these signals by training various DL approaches, including multi-layer perceptron and one- and two-dimensional convolutional neural networks, using the generated dataset. Key findings include the cases where the developed DL approach can resolve signals and provide accurate DOA estimations that the MUSIC algorithm cannot. [ABSTRACT FROM AUTHOR]

The estimation of the direction of electromagnetic (EM) waves from a radio source using electrically short antennas is one of the challenging problems in the field of radio astronomy. In this paper we have developed an algorithm which performs better in direction and polarization estimations than the existing algorithms. Our proposed algorithm Snapshot Averaged Matrix Pencil Method (SAM) is a modification to the existing Matrix Pencil Method (MPM) based Direction of Arrival (DoA) algorithm. In general, MPM estimates DoA of the incoherent EM waves in the spectra using unitary transformations and least square method (LSM). Our proposed SAM modification is made in context to the proposed Space Electric and Magnetic Sensor (SEAMS) mission to study the radio universe below 16 MHz. SAM introduces a snapshot averaging method to improve the incoherent frequency estimation thereby improving the accuracy of DoA estimation. It can also detect polarization to differentiate between Right Hand Circular Polarlization (RHCP), Right Hand Elliptical Polarlization (RHEP), Left Hand Circular Polarlization (LHCP), Left Hand Elliptical Polarlization (LHEP) and Linear Polarlization (LP). This paper discusses the formalism of SAM and shows the initial results of a scaled version of a DoA experiment at a resonant frequency of ∼ 72 MHz. [ABSTRACT FROM AUTHOR]

This paper presents a modified orthogonal propagator method (OPM) with spline interpolation for direction of arrival (DoA) estimation. The conventional OPM is based on the noise-free signal model. When noise exists, the main contribution of noise (additive temporally and spatially white Gaussian noise) is in the diagonal elements of the data covariance matrix. Therefore, the influence of noise can be minimized by restoring the noise free diagonal elements through an interpolation procedure and the propagator can then be directly extracted from the denoised data covariance matrix, which is the main idea of the proposed method in this paper. The performance of the proposed modified OPM is tested through numerical simulations. Simulation results show that the proposed modified OPM achieves low root-mean square errors (RMSEs) with small computational load in DoA estimation. [ABSTRACT FROM AUTHOR]

Self-tracking receivers have been suggested for satellite and mobile communication applications. In this paper, we propose and demonstrate an array receiver (Rx) architecture based on phase-locked loops. The system is capable of automatically tracking a moving source and providing direction-of-arrival (DOA) estimates calculated from array signal phase differences. After deriving the system transfer functions, we show a digital implementation of the receiver and experimentally prove its phase detection capability. In combination with an eight-element linear array and analog front ends, we build a hybrid receiver and demonstrate its DOA estimation performance in static and dynamic outdoor setups. This paper gives the details about theoretic principles, implementation concept, and realization of the proposed receiver. We demonstrate DOA errors below 4° and show the reproducibility of the results. Using dynamic experiments, we verify the tracking ability of the system, which makes it applicable to retrodirective antennas. [ABSTRACT FROM PUBLISHER]

In this paper, a Toeplitz construction method based on eigenvalues and eigenvectors is proposed to combine with traditional denoising algorithms, including fractional low-order moment (FLOM), phased fractional low-order moment (PFLOM), and correntropy-based correlation (CRCO) methods. It can improve the direction of arrival (DOA) estimation of signals in impulsive noise. Firstly, the algorithm performs eigenvalue decomposition on the received covariance matrix to obtain eigenvectors and eigenvalues, and then the Toeplitz matrix is created according to the eigenvectors corresponding to its eigenvalues. Secondly, the spatial averaging method is used to obtain an unbiased estimate of the Toeplitz matrix, which is then weighted and added based on the corresponding eigenvalues. Next, the noise subspace of the Toeplitz matrix is reconstructed to obtain the one that has less angle information. Finally, the DOA of the coherent signal is estimated using the Multiple Signal Classification (MUSIC) algorithm. The improved method based on the Toeplitz matrix can not only suppress the effect of impulsive noise but can also solve the problem of aperture loss due to its decoherence. A series of simulations have shown that they have better performances than other algorithms. [ABSTRACT FROM AUTHOR]

Sparse arrays are widely employed in array signal processing due to their obvious advantages in array element distribution and uniform degrees of freedom (uDOFs). In this paper, a generalized augmented multi-subarray nested array (GAMSNA-I) and its variant, GAMSNA-II are proposed, with the objective of increasing uDOFs and reducing mutual coupling. Based on two subarrays of the prototype nested array (NA), GAMSNA-I is constructed by reconfiguring the dense uniform linear array (ULA) and forward-shifting the sparse ULA. GAMSNA-II is obtained by sparsifying the dense part of GAMSNA-I, ensuring constant uDOFs while further reducing mutual coupling. Subsequently, the closed-form expression for the uDOFs of GAMSNA-I with an arbitrary number of sensors is derived, and the proof is provided that the uDOFs of GAMSNA-II remain unchanged relative to that of GAMSNA-I. Compared to some existing array configurations, both GAMSNA-I and GAMSNA-II exhibit improved uDOFs, with GAMSNA-II achieving lower mutual coupling. Simulation results show the superior performance of the proposed GAMSNA-I and GAMSNA-II. [ABSTRACT FROM AUTHOR]

Traditional direction of arrival (DOA) estimation algorithms typically have poor spatial resolution and robustness. In this paper, we propose a broadband highresolution DOA estimation method based on the generalized weighted Radon transform (GWRT). The array signal can be converted into the frequencywavenumber (f-k) domain using the conditional wavenumber spectrum function (CWSF). Then, a linear integral mathematical model for highresolution DOA estimation is derived by transforming the f-k domain into the azimuth-energy domain using the GWRT. Computer simulation and sea trials were conducted to validate the feasibility and performance of the proposed method. The results obtained indicate that the proposed method yields a lower sidelobe level and can more effectively suppress the output energy in the nontarget direction when compared to the conventional beamforming (CBF), steered minimum variance (STMV), and deconvolution (DCV) methods. Further, the proposed method provides improved spatial resolution and robustness in a multi-target environment. [ABSTRACT FROM AUTHOR]

This paper addresses the problem of the two-dimensional direction-of-arrival (2D DOA) estimation of low-elevation or non-low-elevation targets using L-shaped uniform and sparse arrays by analyzing the signal models' features and their mapping to 2D DOA. This paper proposes a 2D DOA estimation algorithm based on the dilated convolutional network model, which consists of two components: a dilated convolutional autoencoder and a dilated convolutional neural network. If there are targets at low elevation, the dilated convolutional autoencoder suppresses the multipath signal and outputs a new signal covariance matrix as the input of the dilated convolutional neural network to directly perform 2D DOA estimation in the absence of a low-elevation target. The algorithm employs 3D convolution to fully retain and extract features. The simulation experiments and the analysis of their results revealed that for both L-shaped uniform and L-shaped sparse arrays, the dilated convolutional autoencoder could effectively suppress the multipath signals without affecting the direct wave and non-low-elevation targets, whereas the dilated convolutional neural network could effectively achieve 2D DOA estimation with a matching rate and an effective ratio of pitch and azimuth angles close to 100% without the need for additional parameter matching. Under the condition of a low signal-to-noise ratio, the estimation accuracy of the proposed algorithm was significantly higher than that of the traditional DOA estimation. [ABSTRACT FROM AUTHOR]

Direction of arrival (DOA) estimation for conformal arrays is challenging due to non-omnidirectional element patterns and shadow effects. Conical conformal array (CCA) can avoid the shadow effect at small elevation angles. So CCA is suitable for DOA estimation on both azimuth and elevation angles at small elevation angles. However, the element pattern in CCA cannot be obtained by conventional directional element coordinate transformation. Its local element pattern also has connection with the cone angle. The paper establishes the CCA radiation pattern in local coordinate system using 2-D coordinate transformation. In addition, in the case of large elevation angle, only half elements of the CCA can receive signal due to the shadow effect. The array degrees of freedom (DOF) are reduced by halves. We introduce the difference coarray method, which increases the DOF. Moreover, we propose a more accurate propagator method for 2-D cases. This method constructs a new propagation matrix and reduces the estimation error. In addition, this method reduces computational complexity by using linear computations instead of eigenvalue decomposition (EVD) and avoids spectral search. Simulation and experiment verify the estimation performance of the CCA. Both demonstrate the CCA model established in this paper is corresponding to the designed CCA antenna, and the proposed algorithms meet the needs of CCA angle detection. When the number of array elements is 12, the estimation accuracy is about 5 degrees. [ABSTRACT FROM AUTHOR]

This paper proposes a novel coprime array configuration, which achieves more degrees of freedom (DOFs) than the existing coprime arrays for half wavelength array motion in direction-of-arrival estimation. Generally, in a moving coprime array, there exists a large number of redundant lags in its difference coarray, which limits the number of achievable DOFs. In the proposed configuration, we place the sensors of the array strategically so that the redundant lags decrease. The mathematical expression for the number of consecutive lags of the proposed moving coprime array is provided in the paper. There will be a substantial improvement in the number of consecutive DOFs of the proposed moving coprime array over the existing moving coprime arrays. Simulations are carried out to demonstrate the effectiveness of the proposed coprime array over the existing coprime arrays in moving platform. [ABSTRACT FROM AUTHOR]

This paper proposes the generalized MUltiple SIgnal Classification (MUSIC)-like algorithm for robust MUSIC-like processing for underwater applications. The solution proposed in this paper is to generalize the noise correlation assumption and include a noise correlation model in its problem formulation. By doing so, the proposed generalized MUSIC-like algorithm is able to provide robust MUSIC-like performances in any noise condition, so long as the noise correlation property of the environment is known partially. Results from simulations and real data processing show that our proposed algorithm is able to suppress spurious peaks caused by mismatched noise assumptions in standard MUSIC-like algorithms. The bound of the controlling parameter denoted by $\beta $ for the proposed generalized MUSIC-like algorithm is also discussed in this paper. Performance study using Monte Carlo simulations shows that the proposed generalized MUSIC-like algorithm has the same resolving power as the MUSIC method but slightly poorer accuracy in direction-of-arrival (DOA) estimation. This paper also presents the results from real data processing by the generalized MUSIC-like algorithm and demonstrates better resolving power than the Capon and MUSIC algorithms used consistently in the experiment. [ABSTRACT FROM AUTHOR]

This paper points out a critical issue in the study of estimating the azimuth of ground sources by using the polarization characteristics of Rayleigh waves: even if the signal quality is good, the degree of polarization of Rayleigh waves varies across different frequency bands, and the band with the strongest energy is not the one with the lowest azimuth error. A direction of arrival estimation method for ground sources based on optimally polarized Rayleigh waves using a single three-component geophone is presented in this paper. First, the reciprocal ellipse rate, flatness coefficient, and the angle between the semi-minor axes and the horizontal plane are selected as the polarization parameters of this method according to two quantitative principles. Then the frequency band range of the optimal polarization Rayleigh wave is determined by analyzing the sum of the weights of the three polarization parameters in different frequency bands. After filtering and combining with the existing surface wave analysis method, the actual data bearing estimation result with an average error of only 4.95 degrees and a standard deviation of only 1.82 degrees is obtained. It is also found that the signal-to-noise ratio approximates the exponential decay of the direction of arrival error obtained by this method. [ABSTRACT FROM AUTHOR]

The Multiple Signal Classification (MUSIC) algorithm has become one of the most popular algorithms for estimating the direction-of-arrival (DOA) of multiple sources due to its simplicity and ease of implementation. Spherical microphone arrays can capture more sound field information than planar arrays. The collected multichannel speech signals can be transformed from the space domain to the spherical harmonic domain (SHD) for processing through spherical modal decomposition. The spherical harmonic domain MUSIC (SHD-MUSIC) algorithm reduces the dimensionality of the covariance matrix and achieves better DOA estimation performance than the conventional MUSIC algorithm. However, the SHD-MUSIC algorithm is prone to failure in low signal-to-noise ratio (SNR), high reverberation time (RT), and other multi-source environments. To address these challenges, we propose a novel joint spherical harmonic domain beam-space MUSIC (SHD-BMUSIC) algorithm in this paper. The advantage of decoupling the signal frequency and angle information in the SHD is exploited to improve the anti-reverberation property of the DOA estimation. In the SHD, the broadband beamforming matrix converts the SHD sound pressure to the beam domain output. Beamforming enhances the incoming signal in the desired direction and reduces the SNR threshold as well as the dimension of the signal covariance matrix. In addition, the 3D beam of the spherical array has rotational symmetry and its beam steering is decoupled from the beam shape. Therefore, the broadband beamforming constructed in this paper allows for the arbitrary adjustment of beam steering without the need to redesign the beam shape. Both simulation experiments and practical tests are conducted to verify that the proposed SHD-BMUSIC algorithm has a more robust adjacent source discrimination capability than the SHD-MUSIC algorithm. [ABSTRACT FROM AUTHOR]

In this paper, we will discuss a calibration algorithm for a digital antenna array that diagnoses its real performance. It can be applied at such stages of the antenna system life cycle as design, tuning, and especially maintenance. A calibration implementation using a scalar method for a multi-beam digital antenna array is proposed and investigated. On-the-fly calibration ensures a continuous improvement in beam pointing accuracy by reducing internal errors in the receiving (transmitting) channels. The purpose of the study is to experimentally examine the capabilities of digital beamforming to increase the angle-of-arrival estimation accuracy. A simulation model of the receiving antenna was created in an anechoic chamber with a planar antenna positioner. The possibility of precise estimation of the direction of arrival using the digital beamforming with electronic scanning was demonstrated. The proposed simulation model made it possible to observe the convergence of the antenna array calibration process using the proposed method for various errors in the signal paths, as well as different signal-to-noise ratios. It has been proven that even under adverse conditions early in the calibration algorithm, the phase error detection converges with high accuracy, and its value decreases uniformly even to the fractions of an angular degree. [ABSTRACT FROM AUTHOR]

Direction of arrival (DOA) estimation with nested arrays has been widely investigated in the field of array signal processing, but most studies assume that the noise is Gaussian white noise. In practical situations, there may exist impulsive noise (a kind of heavy-tailed noise), wherein the performance of traditional subspace-based DOA estimation algorithms deteriorates significantly. In this paper, we propose a correlation entropy-based infinite norm preprocessing algorithm, which can be applicable to any type of impulsive noise. Each snapshot of the sensor array data is processed by an exponential kernel function with the infinite norm, which can effectively combat the outliers. Furthermore, we construct the equivalent second-order covariance matrix and perform DOA estimation using classical subspace methods. Simulation results demonstrate the effectiveness of the proposed method for both symmetric α -stable distribution and the Gaussian mixture model. [ABSTRACT FROM AUTHOR]

Nowadays, sparse arrays have been a hotspot for research in the direction of arrival (DOA). In order to achieve a big value for degrees of freedom (DOFs) using spatial smoothing methods, researchers try to use multiple uniform linear arrays (ULAs) to construct sparse arrays. But, with the number of subarrays increasing, the complexity also increases. Hence, in this paper, a design method, named as the cross-coarray consecutive-connected (4C) criterion, and the sparse array using Q ULAs (SA-UQ) are proposed. We first analyze the virtual sensor distribution of SA-U2 and extend the conclusions to SA-UQ, which is the 4C criterion. Then, we give an algorithm to solve the displacement between subarrays under the given Q ULAs. At last, we consider a special case, SA-U3. Through the analysis of DOFs, SA-UQ can find underdetermined signals. Moreover, SA-U3 can obtain DOFs close to other sparse arrays using three ULAs. The simulation experiments prove the performance of SA-UQ. [ABSTRACT FROM AUTHOR]

To improve the performance of underdetermined direction of arrival (DOA) estimation in the scenario of strong mutual coupling and unknown nonuniform noise, this paper presents a novel coprime polarization sensitive array (PSA) with limited antenna number and proposes a low-complexity DOA estimation method via iterative covariance matrix reconstruction. The proposed synthetic array is composed of two single-polarized subarrays with dipole or loop antennas. Owing to the polarization domain, it can efficiently reduce the mutual coupling between subarrays, which dominates the effect of mutual coupling in the existing coprime arrays. For effectively eliminating the nonuniform noise, the cross-covariance matrix between subarrays is utilized. Based on it, the full aperture and all degrees of freedoms of the difference coarray with holes are obtained, and then, initial DOAs are estimated by using orthogonal matching pursuit algorithm. The oblique projection operators depending on initial DOAs are constructed to fill holes in difference coarray, in order to generate a larger covariance matrix for refined angle estimation. Then, a fast iterative procedure associated with covariance matrix reconstruction is given to achieve final DOA estimation, for further enhancing estimation performance. Theoretical analysis and simulation results verify the effectiveness of the proposed array and method. [ABSTRACT FROM AUTHOR]

The traditional coprime parallel array (TrCPA) is prone to suffer from the problem of angle ambiguity, due to its larger inter-element spacing and limited array aperture, for two-dimensional direction of arrival estimation. And the classic multiple signal classification (MUSIC) algorithm has heavy complexity and has poor estimation ability in some unsatisfactory situations. Both restrict the improvement of angle estimation performance. In this paper, we design a novel displaced coprime parallel array termed NDCPA, by rearranging and misplacing all subarrays of TrCPA along the coordinate axis, which brings about larger array aperture making contributions to superior angle estimation accuracy. Besides, we propose an improved two-step reduced-dimensional MUSIC algorithm to further enhance angle estimation accuracy. The proposed method reconstructs the covariance matrix, which can fully exploit the information contained in uniform linear subarrays. Meanwhile, the transformation of angle domain divides the original two-dimensional search into two one-dimensional searches, reducing complexity to a certain extent. Finally, simulation results verify the effectiveness and applicability of the proposed configuration and method compared with the other structures and methods. [ABSTRACT FROM AUTHOR]

Nonuniform linear arrays (NLAs) have attracted considerable attention owing to their capability to enhance the degrees of freedom (DOF) and increase the array aperture, which is essential for improving performance in terms of both the direction of arrival estimation and adaptive beamforming. This paper presents two new NLAs, namely interleaved coprime array (ICA) and augmented interleaved array (AIA). The ICA consists of two uniform linear subarrays, whose inter-element spacings are coprime integers. The ICA can obtain more uniform degrees of freedom (uDOF), while maintaining weak mutual coupling effects, because its configuration includes only minority sensors interleaved. The optimal configuration of the ICA is deduced using the principle of maximizing the uDOF. Moreover, the AIA geometry is obtained by removing a redundant element in the ICA and appropriately designing the location of the additional element. For a fixed total number of sensors, the AIA can gain more uDOF and DOF than the ICA, while exhibiting lower mutual coupling effects. The closed-form expressions for the properties of the proposed array structures involving an arbitrary number of sensors are also derived. Numerical simulations are performed to verify the superiority of the proposed arrays over other sparse arrays. [ABSTRACT FROM AUTHOR]

The paper addresses the narrowband direction of arrival estimation problem in the presence of multiplicative noise, namely, the local scatterers affect the propagation channel characteristics. Deep learning-based neural network, composed of autoencoders and softmax layer, has been trained to spatially filter the wave with desired reception angle. When the array receives at the desired angle, the filter warns, its output rises to one; otherwise it falls to zero. The filter's response in different scenarios has been investigated by performing various simulations. It has been observed that for the vast majority of scenarios, the filter can detect the direction, regardless of the exception for channels with severe fading. [ABSTRACT FROM AUTHOR]

In this paper, we propose a novel rearranged coprime array (RCA) configuration for direction-of-arrival (DOA) estimation, which achieves more degrees-of-freedom (DOF) than the existing RCA with the same number of sensors. It is known that RCA is formed by placing additional sensors to fill up the holes in the difference coarray of the thinned coprime array (TCA). Here, we propose a generalized rearranged coprime array (GRCA) configuration, which is obtained by strategically placing extra sensors to fill up the holes in the difference coarray of the generalized thinned coprime array (GTCA). As the GTCA achieves more DOF than the TCA by judiciously choosing its parameters, the proposed GRCA also attains a considerably large number of DOF than the original RCA. The required simulations are carried out to demonstrate the effectiveness and superiority of the proposed GRCA by comparing it with the existing coprime arrays. [ABSTRACT FROM AUTHOR]

Machine learning-based direction-of-arrival (DOA) estimation methods can have a good predictive ability even in complex scenarios. However, their estimation performance in the face of unknown data is poor because they rely on the generalization ability of the algorithm itself. Therefore, this paper proposes a DOA estimation method based on the Light Gradient Boosting Machine (LightGBM) algorithm. Using the histogram algorithm, gradient-based one-sided sampling and exclusive feature bundling measures, the LightGBM algorithm can reduce the time to find the best segmentation point, reduce the amount of data and the number of features in the dataset, thus reducing the model training time, and achieve high prediction accuracy. Applying the LightGBM algorithm to the DOA estimation problem and using a large dataset for training can improve the estimation accuracy while reducing the training cost. Simulation and real experimental results verify the effectiveness of the method. [ABSTRACT FROM AUTHOR]

Aiming at the problem of error in deep-sea DOA (Direction of Arrival, DOA) estimation based on plane wave sound field model, this paper establishes the array signal model of deep-sea DOA estimation under multipath channel based on ray theory. The characterization method of deep-sea multipath ray propagation time and adjacent array element ray propa- gation delay difference are also derived. Compared with the propagation delay difference expression of adjacent array elements in the traditional plane wave model, the propagation delay difference expression of adjacent array elements derived in this pa- per is more universal. Combined with the decoherence DOA estimation algorithm, the performance of deep-sea DOA estima- tion is improved, and the effectiveness of the algorithm is verified by simulation. The research shows that the time delay difference between adjacent array elements is not only related to the distance between array elements and the target azimuth, but also related to the depth of the sound source and the horizontal distance from the sound source to each array element. The construction of the steering vector in DOA estimation should consider the influence of these factors. At this time, DOA esti- mation is a multi-dimensional parameter optimization problem. Fully considering the acoustic propagation characteristics of the ocean sound field can fundamentally solve the error problem of deep-sea DOA estimation. [ABSTRACT FROM AUTHOR]

The objective of this paper is to present the performance of Direction of Arrival(DoA) estimation algorithms for underwater sound source localization using an acoustic Vector Sensor Array (VSA) that is developed by the National Institute of Ocean Technology, Chennai. Algorithms such as conventional beam forming, Multiple Signal Classification (MUSIC) with Eigen value decomposition, and MUSIC with Singular Value Decomposition (SVD) are used for estimation of DoA and performance study. An experiment has been conducted with the VSA at the Acoustic Test Facility of NIOT with the source transmission of 1 kHz to 5 kHz for different azimuth angles. The estimation of DoA using the above three algorithms and the comparison of the results on resolution and accuracy have been studied in detail in terms of the number of vector elements. Results reveal that the MUSIC method gives results with higher accuracy and resolution than the conventional method. The maximum deviation from the true angle in the conventional method is 4°; in MUSIC, it is 2°, whereas in MUSIC with SVD, it is 1°. While the standard MUSIC algorithm involves computing the eigenvectors of the covariance matrix, which can be computationally expensive, MUSIC with SVD provides a more efficient way to achieve better results. SVD enables straightforward computation of the signal subspace, making it more practical for real-time applications like coastal surveillance. Further to the laboratory experiment, the vector sensor system has been deployed in an open sea environment near the harbor and a known source experiment is carried out. The DoA estimated using MUSIC with SVD for the field data reveals that the results are in good comparison with the measured azimuth and elevation positions. The deviations in the field results are due to dynamic conditions of the ocean,and more sea trials need to be carried out for further study. [ABSTRACT FROM AUTHOR]

A spatially polarized time-frequency distribution (SPTFD) based on dual-polarized double-fed antenna arrays is adapted to deal with polarization-unstable signals. A linear time-frequency (TF) representation was used for an instantaneous frequency (IF) estimate, primarily due to its simplicity and immunity to cross-interference. Using a set of linear TF transformations using Gaussian windows and Fourier oscillation kernels, the IF estimated window widths of multiple unstable signals are obtained. This paper introduces a new method for estimating the direction of arrival (DOA) of polarized waves using adaptive linear time-frequency transforms. In this paper, a narrowband far-field point source on the receiving array is analyzed. The source signal is split into two orthogonally polarized components. The optimal window is determined by the first derivative of the IF; for this purpose, we take a simple algorithm for solving the derivative and optimize it. In developing TF-adaptive and fully automatic TF display technology, the first method is to use the time-adaptive window for minimizing the IF estimate mean square error (MSE) sum at each moment, while the second procedure is to adjust according to time and frequency and minimize estimate MSE sum at each position in the TF region. Due to its combination with signal polarization, the spatial time-frequency distribution (STFD) gains more freedom and thus perfects the phonon space estimation of noise and signal. On the SPTFD platform, polarized time-frequency multiple signal classification (PTF-MUSIC) is used for the estimation of signal direction of arrival, which outperforms conventional time-frequency MUSIC. Using the example of a synthesized signal, this method outperforms conventional techniques in DOA estimation. [ABSTRACT FROM AUTHOR]

To address the problem of expensive computation in traditional two-dimensional (2D) direction of arrival (DOA) estimation, in this paper, we propose a 2D DOA estimation method based on a reduced dimension and root-finding MUSIC algorithm for nested planar arrays (NPAs). Specifically, the algorithm proposed in this paper transforms the problem based on 2D spectral peak search into two one-dimensional estimation problems by reducing the dimension, and then transforms the one-dimensional estimation problem into a problem of polynomial root finding. Finally the parameters are paired to realize the 2D DOA estimation. The proposed algorithm not only performs two root finding operations directly according to the 2D spectral function transformation, avoiding the performance degradation caused by intermediate operations, but can also fully exploit the enlarged array aperture offered by NPAs with reduced computational complexity and no need for virtualization. The superiorities of the proposed algorithm in terms of estimation accuracy and complexity are verified by simulations. [ABSTRACT FROM AUTHOR]

In multi-user multiple-input multiple-output (MIMO) systems, a base station requires downlink channel state information for each user to suppress interferences. In time-varying environments, however, channels at the actual transmission time differ from the estimated ones because we have delay. This causes interference and deteriorates the packet error rate performance. To overcome this problem, we previously proposed a channel prediction method based on direction of arrival (DOA) estimation of multipath components obtained with a compressed sensing technique. This method can predict channels with high accuracy when we can assume that user equipment alone moves and the surrounding scatterers are stationary. In real environments, however, this assumption does not hold, and this method cannot be applied. In this paper, we propose a prediction method using two-step compressed sensing without the above assumption. In the first step, we estimate the DOAs of multipath signals. In the second step, we estimate the Doppler frequencies and their complex amplitudes using the estimated DOA information. From these values, we predict the MIMO channels at the actual transmission time. We discuss the performance of this method in this paper. [ABSTRACT FROM AUTHOR]

This paper reports the first use of a 3-D radar imaging for observing E-region field-aligned plasma irregularities (FAIs) in the midlatitude ionosphere. Five carrier frequencies equally spaced between 46.25 and 46.75 MHz were transmitted alternately with consecutive radar pulses, and 20 receivers were employed for receiving the radar echoes. The experiments were carried out using the middle and upper atmosphere radar (34.85°N, 136.10°E), with the radar beams steered to the geographic north and 6.6° north by east, at the zenith angles of 51.0° and 51.5°, respectively. The 2-D imaging with the echoes collected by the 19 of the 20 receivers revealed that in zonal dimension, the off-beam direction of arrival (DOA) of the echo region changed alternately between positive and negative values, which can be attributed to the highly localized FAIs drifting zonally through the radar beam. On the other hand, the off-beam DOA in meridional dimension was negative and positive, respectively, at higher and lower range locations, which were supposed to be due to the meridional drift component of FAIs. A combination of 5 frequencies and 19 receivers achieved a 3-D imaging of the FAI structures, illustrating small-scale FAI striations and bubblelike plasma structures in the radar volume. Moreover, declination of geomagnetic field line was examined from the imaged 3-D brightness distribution in the radar volume; the estimated declination of geomagnetic field line was in agreement with that computed from the International Geomagnetic Reference Field model in 2011. This paper has demonstrated some capabilities of radar imaging for ionospheric investigation. [ABSTRACT FROM AUTHOR]

In this paper, a modified high-efficiency Convolutional Neural Network (CNN) with a novel Supervised Contrastive Learning (SCL) approach is introduced to estimate direction-of-arrival (DOA) of multiple targets in low signal-to-noise ratio (SNR) regimes with uniform linear arrays (ULA). The model is trained using an on-grid setting, and thus the problem is modeled as a multi-label classification task. Simulation results demonstrate the robustness of the proposed approach in scenarios with low SNR and a small number of snapshots. Notably, the method exhibits strong capability in detecting the number of sources while estimating their DOAs. Furthermore, compared to traditional CNN methods, our refined efficient CNN significantly reduces the number of parameters by a factor of sixteen while still achieving comparable results. The effectiveness of the proposed method is analyzed through the visualization of latent space and through the advanced theory of feature learning. [ABSTRACT FROM AUTHOR]